I hate housework, but I do like a tidy and orderly house. Not that I really ever have achieved that, but the ideal seems lovely. . . I cannot possibly keep up with all the housework and homeschool, nor do I want to. And I want to be sure my children know how to manage their own homes in the future. So we share the work, just as we share the money.
Several years ago I thought about the cleaning tasks that really needed doing on a daily or weekly basis. I wrote each one out on a notecard, trying to break down large tasks into smaller steps. (Instead of "clean the refrigerator" I wrote "clean one refrigerator shelf," for instance.) I made a big pile of these. I let my oldest (who was at the time the only child doing this type of chore) select the required number of chores from the stack. She could choose whatever she wanted--I tried to define the chores to be of about equal importance and difficulty (although I've had to refine my definitions over time of course) and whatever she did would be one thing that would at least get done. I think at the time she did one chore of this type each weekday, so she had five cards. If at some point she tired of a chore and wanted to swap out, this was perfectly allowable, but swaps made in the current week apply to the next week's chores. (So you can only swap a card for a chore that's already complete for this week.)
Now I have three children doing these chores. Two of them have two chores a day and one has one. I needed a way to keep track of what was done and undone! So I found some small metal pails that we had lying around, selected one for each child, tied wide ribbon to the handle of each one, stapled the ribbon to the wall, and clipped five clothespins to each ribbon. The cards for each child go in the bucket at the beginning of the week, and as each day's work is done the cards for completed chores get clipped to the ribbon. If they want to do more chores one day, that's fewer chores for a later day. If they want to trade chore cards, they may, with each other or with the master stack.
Oldest now also has responsibility for one room's regular maintenance. At the moment this is the kids' bathroom. I made her a checklist sheet like you would find in a public restroom, with one column per week. At the top are several weekly tasks, then under that a daily list repeated for each weekday. Next to each task is a line for her to initial when the chore is done. It hangs on the bathroom wall on a clipboard with a pen attached! One sheet lasts for four weeks.
I still have to train them in doing their new tasks, supervise and check their work, but this system helps keep things going smoothly and makes sure that many tasks get done that I could never get to and that each child is learning many household chores. They feel in control because they choose which chores to do and when to do them. As much as housework can make any of us happy, this way of handling it works for us.